# Pumping lemma for regular languages

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Pumping lemma for regular languages](https://ocme.evemisslab.com/en/atlas/atlas-pumping-lemma-regular-languages/)

Every regular language has a positive pumping length such that each sufficiently long member word has a split that remains in the language for every pump count.

atlas-pumping-lemma-regular-languages · canonical_mko

[Pumping lemma for regular languages](https://ocme.evemisslab.com/en/mko/mko-pumping-lemma-regular-languages/)

## Prerequisite nodes


- [Regular language](https://ocme.evemisslab.com/en/atlas/atlas-regular-language/)
- [Deterministic finite automaton](https://ocme.evemisslab.com/en/atlas/atlas-finite-automaton/)
- [Mathematical proof](https://ocme.evemisslab.com/en/atlas/atlas-proof/)
- [Pigeonhole principle](https://ocme.evemisslab.com/en/atlas/atlas-pigeonhole-principle/)
- [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/atlas/atlas-quantifier/)
- [Mathematical induction](https://ocme.evemisslab.com/en/atlas/atlas-mathematical-induction/)